The answer to this question is infinitely many solutions so how do you express the answers in terms of z

Question

The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z.

3x−2y+5z=8

2x−3y+4z=15

(x, y, z) = 

Answer 1

I think what they want you to do is to combine these two equations together twice to get two equations: one in terms of x and z and another in terms of y and z. Then you can use those to express x and y in terms of z. For example, if you did this for x, you'd get:

x = (54 - 23z)/13

Then you can use those to write the answer as:

(x, y, z) = ( (54-23z)/13, <y in terms of z>, z )

Can you finish this by finding out what y is in terms of z?